Piezoelectric resonators are known to include various types and shapes of devices produced from various piezoelectric materials. Typical piezoelectric elements consist of substantially rectangular or round plates made from quartz. These piezoelectric resonators are commonly used for frequency control in electronic devices such as, computers, cellular phones, pagers, radios and wireless data devices, etc. Generally, these types of communication devices demand low frequency deviation over temperature. Also, as consumer demand continually drives down the size and cost of this equipment, the need for piezoelectric devices to be smaller and lower cost while maintaining tight temperature performance has become even greater.
Typically, a miniature piezoelectric resonator is rectangular, as this shape is the most easily packaged in a small size. In addition, quartz is the substrate material of choice due to its low cost. In particular, the AT-cut of quartz provides one of the lowest cost substrates while also providing good frequency-temperature performance. An AT-cut plate is defined as a plate cut at a crystallographic angle of about 35.3.degree. rotated about a X axis from a +Z axis to a -Y axis. Although the AT-cut provides good frequency performance over temperature, the modern trend is for tighter and tighter frequency-temperature performance from piezoelectric resonators which has resulted in the use of external temperature compensation schemes being applied to AT-cut quartz resonators.
In manufacturing AT-cut quartz blanks it is customary to test the frequency performance of the resonator over a temperature range of about -30.degree. C. to +85.degree. C. Generally, an ideal AT-cut quartz blank will present a curve 10 with a frequency deviation over this temperature range of less than about 15 ppm, as shown in FIG. 1. Temperature testing of AT-cut resonators produces a third-order frequency-temperature response that is better known in the industry as a Bechmann curve. The Bechmann curve for each resonator is closely dependent on the exact angle cut of the quartz blank, which varies during the quartz blank wafering process. However, the Bechmann curve is also subject to other external influences such as mechanical stress on the quartz blank when it is mounted or when it is plated with electrodes, for example, and to internal influences such as coupling to other modes. Therefore, it is useful to take the measured Bechmann curve of a quartz and reference it back to an associated equivalent theoretical angle cut which would produce that same curve if there were no other influences.
In practice, any deviation from a desired theoretical AT-cut angle during blank processing produces a linear rotation of the Bechmann curve about an inflection temperature 12, inasmuch as the first derivatives with respect to angle of the third-order temperature coefficients of the Bechmann curve are linear for the AT-cut. As a result, the tested frequency-temperature performance curves of a group a AT-cut quartz resonators will produce a mean theoretical AT-cut angle curve 10 having some type of statistical normal distribution about that mean, expressed in terms of angle. For example, a theoretical AT-cut angle of 35.degree. 20' will produce a curve 10 having a total frequency excursion of 14 ppm (+5 to -9 ppm). However, its is typically experienced that a group a quartz resonators present a one-sigma normal distribution 14 of about .+-.1' about the mean angle. In this case, a quartz resonator having a theoretical AT-cut angle at 35.degree. 21' will produce a curve 16 having a total frequency excursion of about 19 ppm (+7 to -12 ppm). For a specification of 20 ppm, this means that about one-sixth of the population will fall outside of the allowable 20 ppm range. This is an unacceptable yield that would require subsequent temperature compensation to correct.
The breadth of the normal distribution can be lessened somewhat by angle control methodologies which rely on physical limitations to the angle at which quartz blanks are cut. For example, better quality saws and lapping machines can be utilized so that less angle variations are produced.
However, even these improvements do not provide resonators with tight enough frequency-temperature performance to satisfy today's radio communication device requirement. In addition, improved wafering processes do not account for other influences such as stress due to depositing electrodes or mounting the resonators, and coupling to other vibrational modes having different temperature characteristics, such as a flexure mode for example. Therefore, it is still industry practice to temperature test each resonator to verify performance. However, temperature testing is time consuming, capital intensive, and represents a major constituent of processing costs.
There is a need for an improved apparatus and method to provide quartz resonators that: (i) are low cost; (ii) improves yields; (iii) tightens the distribution of measured frequency temperature performance; (iv) requires no extra processing; and (v) reduces the need for temperature testing.